Problem $1$:

Figure $1$ shows a site from Assignment $\backslash$#$2-$ Problem $1.$ Use the results from that assignments to help you complete this assignment:

$1.$ Figure $2$ shows the oedometer results for a single stress increment of virgin compression loading from $\backslash (\backslash$sigma$^\{\backslash$prime$\}=1250\backslash )$ psf to $2500$ psf$.$ The sample has an initial thickness of $1$ inch, and porous stone on top and bottom. Determine $\backslash (\backslash$mathbf$\{$c$\}\_\{\backslash$mathrm$\{$v$\}\}\backslash )$ of the sample using Casagrande's Log Time method.

$2.$ Table $1$ gives the permeability for the top gravelly sand layer, the clay layer and the bottom sand$/$fractured bedrock. Do you think that the top and bottom layers provide adequate drainage for the clay to be considered double drained? Consider the impeded drainage plot given in class when answering.

Table $1$: Permeability of soil layers

$3.$ Use Figure $2$ to determine $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$alpha $\backslash$varepsilon$\}\backslash ).$

$4.$ Using $\backslash (\backslash$mathrm$\{$C$\}\_\{$v$\}\backslash )$ and $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$alpha $\backslash$varepsilon$\}\backslash )$ and $\backslash (\backslash$Delta $\backslash$mathrm$\{$H$\}\backslash )$ from assignment $2,$ please calculate settlement vs$.$ time for up to $50$ years for primary consolidation. Plot the results on a $\backslash (\backslash$Delta H $\backslash )$ vs$.\backslash (\backslash$log $(\backslash )$ time$)$ scale.

$5.$ Approximately how long would the developer have to wait in order to construct the building if the maximum settlement the building can accommodate is $2$ inches? $($Assume that the building is very light, and the additional load is negligible$)$

Problem $2$:

Figure $2$: Oedometer results of one load segment

Based on your calculations from Problem $1,$ you observe that it will take an unacceptably long time for settlement to occur before you can start construction. In order to speed the process, you decide to place $10$ ft of fill on your site, which includes a surcharge load, and to install vertical drains. The drains have an effective diameter $\backslash (\backslash$mathrm$\{$d$\}\_\{\backslash$mathrm$\{$w$\}\}=4\backslash )$ in$.$

$1.$ Calculate ultimate settlement for the case with $10$ ft of fill.

$2.$ What drain spacing is required to achieve $\backslash (90\backslash \%\backslash )$ consolidation by the end of $1$ year? You will have to assume a value for $\backslash ($ c$\_\{$v$-$h$\}\backslash )$ based on $\backslash ($ c$\_\{$v$\}\backslash ).$

Six months after the placement of your surcharge you measure $1\mathrm{.}6$ feet of settlement that has occurred, and consolidation is $\backslash (85\backslash \%\backslash )$ complete.

$3.$ Use this data to calculate field calibrated $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}-\backslash$mathrm$\{$h$\}\}\backslash ).$

$4.$ Use same data to update your estimate of ultimate settlement.

$5.$ Assume that the surcharge is removed at $\backslash ($ t$=1$ y r $\backslash ).$ Confirm $($using the calibrated $\backslash (\backslash$mathrm$\{$c$\}\_\{\backslash$mathrm$\{$v$\}-\backslash$mathrm$\{$h$\}\}\backslash ))$ that after $1$ year the primary consolidation will be practically complete. What is the effective OCR following the surcharge removal?

$6.$ Estimate the new $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$alpha $\backslash$overline$\{\}\}\backslash )$ following surcharge removal. Use the updated $\backslash (\backslash$mathrm$\{$C$\}\_\{\backslash$alpha $\backslash$varepsilon$\}\backslash )$ to calculate the amount of settlement between year $1$ and $51.$